Which fraction makes the statement TRUE?

2/10<____________ <7/11

a.6/13
b. 9/9
c. 12/13
d. 1/10

1 answer

Let's evaluate each option to find a fraction that falls between \( \frac{2}{10} \) and \( \frac{7}{11} \).

First, we convert both \( \frac{2}{10} \) and \( \frac{7}{11} \) to decimal for easier comparison:

  • \( \frac{2}{10} = 0.2 \)
  • \( \frac{7}{11} \approx 0.6363 \) (by calculating \( 7 \div 11 \))

Now we have: \[ 0.2 < \text{fraction} < 0.6363 \]

Now, let's convert each option to decimal:

a. \( \frac{6}{13} \): \[ 6 \div 13 \approx 0.4615 \quad (True, \ 0.2 < 0.4615 < 0.6363) \]

b. \( \frac{9}{9} = 1 \): \[ 1 \quad (False, \ 0.2 < 1 \ is\ not\ true) \]

c. \( \frac{12}{13} \): \[ 12 \div 13 \approx 0.9231 \quad (False, \ 0.2 < 0.9231 \ is\ not\ true) \]

d. \( \frac{1}{10} \): \[ \frac{1}{10} = 0.1 \quad (False, \ 0.1 < 0.2 \ is\ not\ true) \]

Thus, the only fraction that makes the statement true is:

a. \( \frac{6}{13} \).